Limits of PGL(3)-translates of plane curves, II

Abstract

Every complex plane curve C determines a subscheme S of the P 8 of 3×3 matrices, whose projective normal cone (PNC) captures subtle invariants of C . In [P. Aluffi, C. Faber, Limits of PGL(3)-translates of plane curves, I, J. Pure Appl. Algebra 214 (5) (2010) 526–547] we obtain a set-theoretic description of the PNC and thereby we determine all possible limits of families of plane curves whose general element is isomorphic to C . The main result of this article is the determination of the PNC as a cycle; this is an essential ingredient in our computation in [P. Aluffi, C. Faber, Linear orbits of arbitrary plane curves, Michigan Math. J. 48 (2000) 1–37] of the degree of the PGL ( 3 ) -orbit closure of an arbitrary plane curve, an invariant of natural enumerative significance.